Determination of particle-size distributions from light-scattering measurement using Lucy-Richardson algorithm

Yang, Fugui; Wang, Anting; Dong, Lei; Ming, Hai

doi:10.1117/1.oe.52.4.043605

Cited by 3 publications

(2 citation statements)

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“…The method described there is equivalent to the Lucy-Richardson method (Richardson, 1972;Lucy, 1974). The method has been applied for calculating a size distribution from scattering data by several authors (Yang et al, 2013;Benvenuto et al, 2016;Benvenuto, 2017;Bakry et al, 2019). Although the convergence of the iterative EM algorithm is ensured since the algorithm is guaranteed to increase the likelihood with each iteration, a stable solution cannot be obtained because of its ill-posed nature and because an additional stabilization mechanism is required.…”

Section: Regularization Techniquesmentioning

confidence: 99%

“…The strategy of using analytical expressions for the size distribution may limit the model too much to give a reasonable agreement with the data. To overcome this issue, regularization techniques (Lucy, 1974(Lucy, , 1994Glatter, 1977;Svergun, 1992;Yang et al, 2013) and Monte Carlo methods have been used (Krautha ¨user et al, 1996;Breßler et al, 2015), mainly due to the lack of flexibility of available analytical probability distribution functions (PDFs).…”

Section: Introductionmentioning

confidence: 99%

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Updates inSASfitfor fitting analytical expressions and numerical models to small-angle scattering patterns

Kohlbrecher¹,

Breßler²

2022

J Appl Crystallogr

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Small-angle scattering is an increasingly common method for characterizing particle ensembles in a wide variety of sample types and for diverse areas of application. SASfit has been one of the most comprehensive and flexible curve-fitting programs for decades, with many specialized tools for various fields. Here, a selection of enhancements and additions to the SASfit program are presented that may be of great benefit to interested and advanced users alike: (a) further development of the technical basis of the program, such as new numerical algorithms currently in use, a continuous integration practice for automated building and packaging of the software, and upgrades on the plug-in system for easier adoption by third-party developers; (b) a selection of new form factors for anisotropic scattering patterns and updates to existing form factors to account for multiple scattering effects; (c) a new type of a very flexible distribution called metalog [Keelin (2016). Decis. Anal. 13, 243–277], and regularization techniques such as the expectation-maximization method [Dempster et al. (1977). J. R. Stat. Soc. Ser. B (Methodological), 39, 1–22; Richardson (1972) J. Opt. Soc. Am. 62, 55; Lucy (1974). Astron. J. 79, 745; Lucy (1994). Astron. Astrophys. 289, 983–994], which is compared with fits of analytical size distributions via the non-linear least-squares method; and (d) new structure factors, especially for ordered nano- and meso-scaled material systems, as well as the Ornstein–Zernike solver for numerical determination of particle interactions and the resulting structure factor when no analytical solution is available, with the aim of incorporating its effects into the small-angle scattering intensity model used for fitting with SASfit.

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Section: Regularization Techniquesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Updates inSASfitfor fitting analytical expressions and numerical models to small-angle scattering patterns

Kohlbrecher¹,

Breßler²

2022

J Appl Crystallogr

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SiNPs Decoration of Silicon Solar Cells and Size Analysis on the Downshifting Mechanism Response for the Enhancement of Solar Cells Efficiency

Ramos-Carrazco,

de la Cruz-Arreola,

Martínez-Zamora

et al. 2024

Silicon

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Inversion method based on stochastic optimization for particle sizing

et al. 2016

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A stochastic inverse method is presented based on a hybrid evolutionary optimization algorithm (HEOA) to retrieve a monomodal particle-size distribution (PSD) from the angular distribution of scattered light. By solving an optimization problem, the HEOA (with the Fraunhofer approximation) retrieves the PSD from an intensity pattern generated by Mie theory. The analyzed light-scattering pattern can be attributed to unimodal normal, gamma, or lognormal distribution of spherical particles covering the interval of modal size parameters 46≤α≤150. The HEOA ensures convergence to the near-optimal solution during the optimization of a real-valued objective function by combining the advantages of a multimember evolution strategy and locally weighted linear regression. The numerical results show that our HEOA can be satisfactorily applied to solve the inverse light-scattering problem.

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Determination of particle-size distributions from light-scattering measurement using Lucy-Richardson algorithm

Cited by 3 publications

References 0 publications

Updates inSASfitfor fitting analytical expressions and numerical models to small-angle scattering patterns

Updates inSASfitfor fitting analytical expressions and numerical models to small-angle scattering patterns

SiNPs Decoration of Silicon Solar Cells and Size Analysis on the Downshifting Mechanism Response for the Enhancement of Solar Cells Efficiency

Inversion method based on stochastic optimization for particle sizing

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